Is there an advantage to Lightning/Stellar as compared to Lightning/Bitcoin? I understand that Stellar has far better speed than Bitcoin, but with Lightning being used as the transaction layer, does that speed difference matter?
And the speed difference you mention is an important point - so many of these coins have acted as artificial capacity surrogates during Bitcoin's scaling woes. But with LN, I don't see their use at all...
Even things like smart contracts can be integrated into Bitcoin (I believe the Bitcoin Cash camp is working on this)
Some prefer to avoid LN if possible, especially as its topology may turn out to be not as p2p as people prefer, and LN nodes may be operated by corporations who may or may not have KYC regulations that people would like to avoid. Besides this, there are general PoS vs PoW differences--some consider PoW an undesirable waste of energy while others consider it a way to secure the network.
Also — Lightning reduces fees and transaction times, but these costs still matter. The time and cost to open and later close a payment channel is a multiple of the latency and transaction cost of the underlying chain. Not very transaction will need a new payment channel, but other things being equal (in particular: connectivity of the Lightning graphs, average transactions per payment channel), the network with lower non-Lightning costs will have proportionally lower Lightning costs too. The cost matters when there’s lots of transactions; the latency makes a difference to both mean and worst-case Lightning transaction and settlement time.
Stellar also uses less energy.
Bitcoin is the slow part of on-chain atomic swaps, so that could be a reason to implement lightning for tokens that already have fast transactions.
If all the LN implementations match, then I could, for example, pay with Bitcoin on LN to a node that will convert it to Litecoin at a given price, then will send that payment to the vendor's node who will accept Litecoin as payment.
That gives a massive incentive for altcoins to support and match the Bitcoin lightning-network APIs exactly, as then it becomes much easier for them to gain market share based on their other qualities (like stability, security, decentralization, longevity, etc...)
With the lighting network you still have to make 2 on chain transactions. 1 to establish the initial channel, and 1 to close it.
And this is PER channel that you establish.
These transaction fees could be quite high, if history is to be used as an example (only a couple months ago, fees hit something like 40 USD).
If you don't want to make frequent 'top up' transactions to what is effectively a hot wallet, then you'd have to lock away many thousands of dollars.
Transaction fees on chain still matter quite a lot if you are unwilling to lock away a whole bunch of money up front.
Also the more money that is locked away on the LN, the more vulnerable to attack it is.
This is because one can attack the network by DDoSing the main chain, such that blocks are full for the time lock period. IE, if someone cheats and publishes an old LN transaction history, you have to publish your anti cheat transaction and if blocks are full for the couple weeks, then you can't defend yourself.
This style of attack only works if there is a bunch of money in the network though.
It is also counteracted if the main chain has high capacity as it becomes that much more expensive to attack the main chain.
EDIT: Proposing an answer to my own question, perhaps LN transaction fees could be significantly lower if using Stellar rather than Bitcoin as the supporting blockchain? If so, does anyone have any estimates regarding the difference?
EDIT 2: It does seem that there would be an advantage to Stellar at the time a channel is closed, since the fee for the underlying blockchain transaction should be significantly less.
But Stellar will be supporting state channels in addition to payment channels, (presumably) allowing for even faster exchange operations (buy/sell market and limit orders) and path payments across multiple currencies, neither of which LN on Bitcoin can do (at least for now).